What is the Greatest Common Factor of 39914 and 39928?

Greatest common factor (GCF) of 39914 and 39928 is 14.

GCF(39914,39928) = 14

We will now calculate the prime factors of 39914 and 39928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39914 and 39928.

How to find the GCF of 39914 and 39928?

We will first find the prime factorization of 39914 and 39928. After we will calculate the factors of 39914 and 39928 and find the biggest common factor number .

Step-1: Prime Factorization of 39914

Prime factors of 39914 are 2, 7, 2851. Prime factorization of 39914 in exponential form is:

39914 = 2¹ × 7¹ × 2851¹

Step-2: Prime Factorization of 39928

Prime factors of 39928 are 2, 7, 23, 31. Prime factorization of 39928 in exponential form is:

39928 = 2³ × 7¹ × 23¹ × 31¹

Step-3: Factors of 39914

List of positive integer factors of 39914 that divides 39914 without a remainder.

1, 2, 7, 14, 2851, 5702, 19957

Step-4: Factors of 39928

List of positive integer factors of 39928 that divides 39914 without a remainder.

1, 2, 4, 7, 8, 14, 23, 28, 31, 46, 56, 62, 92, 124, 161, 184, 217, 248, 322, 434, 644, 713, 868, 1288, 1426, 1736, 2852, 4991, 5704, 9982, 19964

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39914 and 39928. The biggest common factor number is the GCF number.
So the greatest common factor 39914 and 39928 is 14.

Also check out the Least Common Multiple of 39914 and 39928